Twitter Inc. cofounder Jack Dorsey came to Cambridge Monday on a recruitment drive. He is looking to lure a few Massachusetts Institute of Technology graduates back to California to help him quickly grow his latest innovation: a mobile payments company called Square Inc.

The three-year-old start-up is already one of the early leaders in the fast-growing “mobile wallet” marketplace, which includes tech giants such as Google Inc. and local upstarts like Scvngr, to let consumers make purchases with their smartphones instead of using cash or credit cards.

“Square is going after a very big problem, which is commerce,” said Dorsey ahead of a meeting with students at MIT’s Stata Center. “We have a very large ambition for what we want to do, and also the speed with which we want to do it.”

The 400-person company based in San Francisco is looking to double in size over the next year, said Dorsey, as it prepares to expand into overseas markets and grow its customer base of 2 million merchants and small business owners that use its credit card readers for turning tablet computers or smartphones into mobile payment terminals.

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Square has already grown quickly. The amount of money it processes through its payment system grew from $1 billion in 2011 to $8 billion this year. In the Boston area, it has 6,000 business customers, from food truck operators like the Bon Me Truck that sells Vietnamese sandwiches downtown to Toscanini’s Ice Cream in Central Square.

John Blanding/Globe Staff

Twitter cofounder Jack Dorsey was in Cambridge Monday to recruit for his new company.

The company charges users of its card reader a 2.75 percent fee per swipe without many of the additional fees associated with traditional point-of-sale systems. It also makes a smartphone app so that consumers can use their phone when paying at businesses that use Square.

“We are doing what our customers want,” said Toscanini’s co-owner, Gus Rancatore, noting that his shop draws lots of tech-savvy customers from nearby MIT who want to pay with their smartphones. And, what is more, he said, Square provides businesses with a simpler way to process payments.

But even with the explosive growth of mobile wallet technology, the total number of payments being conducted with smartphones is just a fraction of all retail transactions. Although Square processes $8 billion in payments annually, in August alone the US Census Bureau expects retail and food sales to top $400 billion.

“What isn’t happening yet is broad adoption from consumers,” said Denée Carrington, an analyst at Forrester Research in Cambridge. But that is beginning to change slowly because, she said, “the phone is increasingly becoming a shopping companion.”

Fifty percent of smartphone owners say they are interested in using their devices to make payments, according to a recent Forrester report on mobile payments. And younger users express more willingness to pay with their phones.

The interest among early adopters is what is fueling this battle among upstart companies like Square and more established technology companies such as Google Inc. and Amazon.com Inc. to dominate the mobile wallet market, she said. Square’s growth has attracted lots of interest from investors, traditional retailers, and banks. Earlier this month, it completed a $200 million round of fund-raising with backing from Starbucks Coffee Co., which plans to use Square to handle credit card payments at its shops, and Citi Ventures, the investment division of the financial services company. So far, Square has raised more than $300 million.

Dorsey said traditional financial companies such as Citi Ventures and Visa Inc., another Square investor, are funding the company because they want to fuel innovation in a sector that has been slow to adopt technological change. What is more, he said, Square is giving many small-business operators, such as artists or hairdressers, who previously would not be able to afford costly credit card systems, the ability to start accepting plastic.

The Boston start-up Scvngr considers Square its biggest competition as it vies to win over consumers and merchants for its Level Up mobile payments platform, which is used at almost 700 locations around Boston. In July, Scvngr eliminated the swipe fees for card transaction in an effort to attract more customers.

“Square and Level Up, at the end of the day, are going after the same thing,” said Scvngr’s chief executive, Seth Priebatsch. “We suddenly have the ability through mobile devices to change the economics of moving money.”

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